A) \[{{27}^{o}}C\]
B) \[{{40.3}^{o}}C\]
C) \[{{23.3}^{o}}C\]
D) \[{{33.3}^{o}}C\]
Correct Answer: D
Solution :
First Case: \[\therefore \] \[\frac{{{50}^{o}}-{{45}^{o}}}{5}=\left( \frac{{{50}^{o}}+{{45}^{o}}}{2}-{{T}_{0}} \right)\] ? (1) \[{{T}_{0}}=\]temperature of surrounding Second Case: \[\frac{{{45}^{o}}-{{41.5}^{o}}}{5}=K\left( \frac{{{45}^{o}}+{{41.5}^{o}}}{2}-{{T}_{0}} \right)\] ? (2) Dividing equation (1) by equation (2) \[\frac{{{50}^{o}}-{{45}^{o}}}{{{45}^{o}}-{{41.5}^{o}}}=\frac{\left( \frac{{{50}^{o}}+{{45}^{o}}}{2}-{{T}_{0}} \right)}{\left( \frac{{{45}^{o}}+{{41.5}^{o}}}{2}-{{T}_{0}} \right)}\] On solving, we get\[{{T}_{0}}={{33.3}^{o}}C\]
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